Hydrodynamics of slender bodies: applications in offshore engineering
Dr R.C.T. Rainey
W.S. Atkins
Offshore structures contain many slender tubular members, subject to wave loads. The traditional
empirical formula for the wave load is "Morison's equation", which has an inertial term proportional to the
water acceleration, and a drag term proportional to the square of the water velocity.
Both have been refined in recent years, encouraged, at least in part, by the late Sir James Lighthill [1].
The inertial term describes the load in an idealised wakeless flow, and so may be calculated exactly using
the classical techniques of slender body theory [2]. This leads [3,4] to an additional load proportional to
the velocity gradient, and to point loads at member ends and surface intersections. These are important, for
example, in the phenomenon of "ringing" [5], which is a burst of structural vibration produced by the crests
of very steep waves.
The drag term describes the effect of the wake, and has also been refined, for example to model the effects
of vortex shedding. An interesting recent example is the case of a rotating drillstring, in which it is also
necessary to model the steady cross-flow "Magnus" force, which can lead to a whirling instability.
References
[1] Lighthill, Sir James 1979 Waves and hydrodynamic loading. Proc. 2nd Int. Conf. on the Behavoiur of
Offshore Structures. Vol 1 pp 1-40. Cranfield: BHRA Fluid Engineering.
[2] Batchelor, G.K. 1967 An intoduction to fluid dynamics, section 6.9. Cambridge: University Press
[3] Rainey, R.C.T. 1989 A new equation for calculating wave loads on offshore structures. J. Fluid Mech. Vol
204 pp 295-324
[4] Rainey, R.C.T. 1995 Slender-body expressions for the wave load on offshore structures. Proc. R. Soc.
Lond. Vol 450 pp 391-416
[5] Chaplin, J.R., Rainey, R.C.T. & Yemm, R.W. 1997 Ringing of a vertical cylinder in waves. J. Fluid
Mech. Vol 350 pp 119-147
